Periodogram power spectral density estimate

`pxx = periodogram(x)`

`pxx = periodogram(x,window)`

`pxx = periodogram(x,window,nfft)`

`[pxx,w] = periodogram(___)`

`[pxx,f] = periodogram(___,fs)`

`[pxx,w] = periodogram(x,window,w)`

`[pxx,f] = periodogram(x,window,f,fs)`

`[___] = periodogram(x,window,___,freqrange)`

`[___,pxxc] = periodogram(___,'ConfidenceLevel',probability)`

```
[rpxx,f]
= periodogram(___,'reassigned')
```

```
[rpxx,f,pxx,fc]
= periodogram(___,'reassigned')
```

`[___] = periodogram(___,spectrumtype)`

`periodogram(___)`

returns the periodogram power spectral density (PSD) estimate,
`pxx`

= periodogram(`x`

)`pxx`

, of the input signal, `x`

, found
using a rectangular window. When `x`

is a vector, it is
treated as a single channel. When `x`

is a matrix, the PSD is
computed independently for each column and stored in the corresponding column of
`pxx`

. If `x`

is real-valued,
`pxx`

is a one-sided PSD estimate. If
`x`

is complex-valued, `pxx`

is a
two-sided PSD estimate. The number of points, `nfft`

, in the
discrete Fourier transform (DFT) is the maximum of 256 or the next power of two
greater than the signal length.

uses `pxx`

= periodogram(`x`

,`window`

,`nfft`

)`nfft`

points in the discrete Fourier transform (DFT).
If `nfft`

is greater than the signal length,
`x`

is zero-padded to length `nfft`

.
If `nfft`

is less than the signal length, the signal is
wrapped modulo `nfft`

and summed using
`datawrap`

. For example, the input signal ```
[1 2 3
4 5 6 7 8]
```

with `nfft`

equal to 4 results in
the periodogram of `sum([1 5; 2 6; 3 7; 4 8],2)`

.

`[`

returns a frequency vector, `pxx`

,`f`

] = periodogram(___,`fs`

)`f`

, in cycles per unit time. The
sample rate, `fs`

, is the number of samples per unit time. If
the unit of time is seconds, then `f`

is in cycles/second
(Hz). For real-valued signals, `f`

spans the interval
[0,`fs`

/2] when `nfft`

is even and
[0,`fs`

/2) when `nfft`

is odd. For
complex-valued signals, `f`

spans the interval
[0,`fs`

). `fs`

must be the fourth
input to `periodogram`

. To input a sample rate and still use
the default values of the preceding optional arguments, specify these arguments
as empty, `[]`

.

`[`

returns the two-sided periodogram estimates at the frequencies specified in the
vector. The vector `pxx`

,`f`

] = periodogram(`x`

,`window`

,`f`

,`fs`

)`f`

must contain at least two elements,
because otherwise the function interprets it as `nfft`

. The
frequencies in `f`

are in cycles per unit time. The sample
rate, `fs`

, is the number of samples per unit time. If the
unit of time is seconds, then `f`

is in cycles/second
(Hz).

`[___,`

returns the `pxxc`

] = periodogram(___,'ConfidenceLevel',`probability`

)`probability`

× 100% confidence
intervals for the PSD estimate in `pxxc`

.

`[___] = periodogram(___,`

returns the PSD estimate if `spectrumtype`

)`spectrumtype`

is specified as
`'psd'`

and returns the power spectrum if
`spectrumtype`

is specified as
`'power'`

.

`periodogram(___)`

with no output arguments
plots the periodogram PSD estimate in dB per unit frequency in the current
figure window.

[1] Fulop, Sean A., and Kelly Fitz. “Algorithms for computing the
time-corrected instantaneous frequency (reassigned) spectrogram, with
applications.” *Journal of the Acoustical Society of
America*. Vol. 119, January 2006, pp. 360–371.

[2] Auger, François, and Patrick Flandrin. “Improving the Readability of
Time-Frequency and Time-Scale Representations by the Reassignment Method.”
*IEEE ^{®} Transactions on Signal Processing*. Vol. 43, May 1995,
pp. 1068–1089.